Repeat the preceding problem if the currents flow in opposite directions.

Name: Problem 75, Chapter 18: Essential College Physics
Uploaded: 2021-11-11T22:13:33-08:00
Duration: 9 min 53 s
Channel: Linda Winkler
Description: Repeat the preceding problem if the currents flow in opposite directions.

Repeat the preceding problem if the currents flow in...

Key Concepts

Electric Current

Electric current is the flow of electrical charge through a conductor. Its magnitude and direction are critical in the analysis of electromagnetic effects. The direction of the current not only dictates the way in which charges move but also significantly influences the resulting magnetic fields produced around the conductor.

Magnetic Field

A magnetic field is generated around any current-carrying conductor, with both its intensity and orientation being functions of the magnitude and direction of the current. Techniques such as the Biot–Savart law and Ampère’s law help in quantitatively determining these fields, and any changes in current direction will alter the field configuration.

Right-Hand Rule

The right-hand rule is a fundamental tool in electromagnetism used to determine the direction of the magnetic field around a current-carrying wire. By aligning the thumb of the right hand with the current’s direction, the curl of the fingers indicates the orientation of the magnetic field, which is especially important when comparing fields generated by currents flowing in opposite directions.

Superposition Principle

The superposition principle states that the net effect of several influences, such as magnetic fields, is the vector sum of the individual effects. When dealing with multiple current-carrying conductors, this principle is used to calculate the resultant magnetic field at any given point, taking into account contributions from each current source.

Current Direction and Interaction

The direction of current flow directly affects how multiple magnetic fields interact. Currents flowing in the same direction tend to produce magnetic fields that reinforce each other, while currents flowing in opposite directions can lead to cancellation or reversal of the resulting field. Understanding these interactions is crucial when analyzing modifications to systems, such as reversing current directions.

Transcript

00:02 Magnetic fields, so you get the magnitude of the magnetic field of a long straight wire using amper's law.

00:11 And this gives us the relationship that the magnetic field strength is equal to the permeability of free space, mu not, times the current i, divided by 2 pi times the distance.

00:32 Between the observation point and the wire.

00:35 So this is for a long wire.

00:40 To get the direction of the magnetic field, you would use the right -hand rule, placing your thumb along the current, and your fingers make circles around the wire in the direction of the magnetic field.

00:56 But the other thing to realize is that if you have multiple wires or multiple sources of magnetic field, you simply add up the individual contributions from each of the sources.

01:11 And magnetic field is a vector, so you need to be a little bit careful about directions.

01:17 The other thing about long wires is that they do exert a magnetic force, well, magnetic field will exert a force on a long wire in the amount il, l being the direction of current flow along the wire, and the magnitude of l being the length crossed into the magnetic field.

01:44 So as an example of this, we have two wires each carrying the same current, we'll call them wire one and wire two, and we will orient the top wire carrying the current to the right, bottom wire carrying current to the left.

02:04 And there are a couple of points that we want to find.

02:07 The total magnetic field at a and b.

02:12 And then we will find the force they exert on each other.

02:18 So that's kind of the process, but it would be good if we use the right -hand rule.

02:24 And for the top wire, what we have is its magnetic field is coming out of the board at the top and going in at the bottom.

02:35 And of course, there's a wrap -around, a certain, around that.

02:41 The bottom wire, it's the opposite, so it goes in on the top, two goes into the board, on top of the wire, and out of the board on the bottom.

02:58 And again, we have a circulation around the wire of those magnetic fields.

03:06 So at a, what we can see is at point a, the magnetic fields add together they are both into the page and so we would add the strength of both of them together to get the full strength and we know the distance and the current in each wire equal distance and that r is 0 .0075 meters and multiply by two because they each have the same strength at that point being midway.

04:00 Now the permability of free space is 4 pi times 10 to the minus seventh in the si units.

04:10 The current is 2 .5 amps.

04:14 That is an si unit, so perfectly good to include 2 .5 amps, and then multiply by 2, divide by 2 pi.

04:28 Yes, that usually works with the top and divide by 7 .5 millimeters will give us the total magnetic field strength in terms of tesla's.

04:59 And that will give us 1 .33 times 10 to the minus 4 tesla.

05:11 Looking at observation point b, what we have is b1.

05:16 The further wire is going into the page.

05:22 B1 goes into the page and it is weaker.

05:28 B2 is coming out of the page, and it is stronger because it is closer...